title: Coupled van der Pol oscillators
description:
date: 2020-04-30
tags:
layout: layouts/post.njk
Coupled van der Pol oscillators https://scholarsarchive.library.albany.edu/cgi/viewcontent.cgi?article=1004&context=honorscollege_physics
$ g' = A sin Ļt ā γg ā Ļ^2_0 z$
$z' = g$
from models.coupled.vanderpol import *
hv.notebook_extension()
van=get_plot()
van[0]
van
Ļ0 = 2500
ν = 100
µ = 10
Ļ2 = 300*25#554.365
A2=0
def deriv (y,t,A1,Ļ1):
sine1=A1*np.sin(Ļ1 * t)
sine2=A1*np.sin(Ļ2 *t)
zprime = y[1]
gprime = -ν *y[1]*(y[0]**2 - µ) - (Ļ0**2) * y[0] + sine1 + sine2
return np.array([ zprime , gprime, sine1 ])
plt.figure()
y = odeint(deriv, [0.1,0.1,0.], np.linspace(0, 1., 600000),args=(5e6, 2200)) # with w0=2500, get resonance or beating
plot_and_play(y)
plt.figure()
y = odeint(deriv, [0.1,0.1,0.], np.linspace(0, 1., 600000),args=(5e6, 2200)) # with w0=2500, get resonance or beating
plot_and_play(y)
import os
name='vanderpol_coupled_standalone'
path='~/mmy/jup/models/'
os.system(f'jupyter nbconvert {path}{name}.ipynb --to markdown --output {path}{name}')
os.system(f'jupyter nbconvert {path}{name}.ipynb --to markdown --output {path}{name}')